Preheat the oven to 180°C (350°F).
In a large skillet, heat olive oil over medium heat. Add chopped onion and sauté until translucent.
Add minced garlic to the skillet and cook for an additional minute.
Stir in the ground beef, breaking it apart with a spoon. Cook until browned.
Mix in the diced carrots, frozen peas, Worcestershire sauce, thyme, salt, and pepper. Cook for another 5 minutes.
Remove the skillet from heat and let the mixture cool slightly.
Prepare the pie crust by fitting one layer into a pie dish. Pour in the meat filling evenly.
Cover with the second pie crust, sealing the edges tightly. Cut slits in the top crust to allow steam to escape.
Brush the top crust with beaten egg for a glossy finish.
Bake in the preheated oven for 45-50 minutes until the crust is golden brown.
Let the pie rest for 10 minutes before slicing and serving.